Liverpool is one of four authorities that has volunteered to experiment with devolved power from Whitehall. Photograph: David Kendall/PA

David Cameron will announce this morning that he hopes to liberate four areas from the strictures of red tape and central government as he attempts to deliver his idea of the "Big Society".

Liverpool, the Eden Valley in Cumbria, Windsor and Maidenhead in Berkshire and Sutton in south-west London will become "vanguard communities". All four authorities approached the government to experiment with running the parts of their public services they think they can administer better.

They may have central government budgets handed over to them to administer at street level, attempt to improve local transport links themselves, take over command of local assets such as pubs and community services, have a greater say over planning permission or local transport and, in the case of Liverpool, allow volunteers to keep a popular local museum open for longer hours.

Cameron will say in a speech in Liverpool: "Yes, there will be problems – financial problems, legal problems, bureaucratic problems. Yes, there will be objections – local objections, objections from vested interests. But you know what? We're happy about that. This process is all about learning. It's about pushing power down and seeing what happens. It's about unearthing the problems as they come up on the ground and seeing how we can get round them. It's about holding our hands up, saying 'We haven't got all the answers. Let's work them out, together.'"

The government will also announce the creation of a "Big Society Bank" to help finance social enterprises, charities and voluntary groups. The money will come from dormant bank and building society accounts – the amount is thought to be as much as £400m.

The "Big Society" is Cameron's passion, he will say, in contrast to unpopular things he must do out of duty like cutting the deficit. "These four vanguard communities will be the great training grounds of this change; the first territory on which real and ultra-local power is a reality – and the 'Big Society' is built.

"For a long time, the way government has worked – top-down, top-heavy, controlling – has frequently had the effect of sapping responsibility, local innovation and civic action. It has turned many motivated public-sector workers into disillusioned, weary puppets of government targets.

"It has turned able, capable individuals into passive recipients of state help with little hope for a better future. It has turned lively communities into dull, soulless clones of one another. So we need to turn government completely on its head. The rule of this government should be this: if it unleashes community engagement, we should do it; if it crushes it, we shouldn't.

"If this approach isn't like what you've heard from government before, that's because it's not. This is not an initiative. We have not hired a czar. These are not pilots that will be rolled out. This is a big advance for people power."

Labour leadership contender Ed Miliband, who also spent a portion of his career in government as the minister for the third sector, today accused the Conservative party of "cynically attempting to dignify its cuts agenda by dressing up the withdrawal of support with the language of reinvigorating civic society".